Eukaryotic DNA is spatially organized in a hierarchical manner starting from single nucleosomes folded into the higher-order chromatin structures. The DNA trajectory at the second level of organization, in 30-nm fibers, still remains unknown. To tackle this problem, we computed all possible configurations of chromatin fibers with DNA linkers L = 10 - 70 bp (nucleosome repeat length, NRL = 157 - 217 bp). For the first time, we observed two different families of conformations characterized by different DNA topologies. The optimal geometry of a fiber depends on the linker length: the fibers with linkers L = 10n and 10n+5 bp have DNA linking numbers per nucleosome delta(Lk) = -1.5 and -1.0, respectively. In other words, the level of DNA supercoiling is directly related to the nucleosome spacing in chromatin. This theoretical prediction was corroborated by topological gel assays indicating that the DNA supercoiling differs by as much as 50% in nucleosomal arrays with linkers L = 20 and 25 bp, in excellent agreement with our computations. Thus, we made an important step toward resolving the long-standing discrepancy known as the linking-number paradox. We hypothesize that topological polymorphism of chromatin fibers described above may play a role in the process of transcription, which is known to generate different levels of DNA supercoiling upstream and downstream from RNA polymerase. A genome-wide analysis of the NRL distribution in active and silent yeast genes confirmed this assumption. Our results may reflect a general tendency of chromosomal domains containing active or repressed genes to retain topologically distinct higher-order structures. We also analyzed nucleosomal arrays with linkers containing curved DNA fragments, A-tracts. This is important for elucidating contribution of linker DNA conformation and flexibility to nucleosome chain folding and accessibility of DNA in chromatin, because nucleosome linkers are enriched with the A-tracts. Linker DNA conformational variability has been proposed to direct nucleosome array folding into more or less compact chromatin fibers but direct experimental evidence for such models are lacking. We tested this hypothesis by designing nucleosome arrays with A-tracts at specific locations in the nucleosome linkers to induce inward (AT-IN) and outward (AT-OUT) bending of the linker DNA. Using electron microscopy and analytical centrifugation, we observed spontaneous folding of AT-IN nucleosome arrays into highly compact structures, comparable to those induced by linker histone H1. In contrast, AT-OUT nucleosome arrays formed less compact structures with decreased nucleosome interactions similar to wild-type nucleosome arrays. Electron microscopy analysis and Monte Carlo simulations are consistent with a profound zigzag linker DNA configuration and closer nucleosome proximity in the AT-IN arrays due to inward linker DNA bending. We propose that the evolutionary preferred positioning of A-tracts in DNA linkers may control chromatin higher-order folding and thus influence cellular processes such as gene expression, transcription and DNA repair. Indeed, the chromatin folding regulates accessibility of the DNA-encrypted genetic information for transcription factors (TFs), as indicated by a strong difference between the restriction nuclease digestion of nucleosome linkers in AT-IN and AT-OUT arrays. In addition, genomic DNA is made accessible by partial unwrapping of nucleosomes. As follows from the force spectroscopy measurements, the chromatin fiber is so mobile that nucleosomes lose their stacking under small external forces F = 2-3 pN, whereas at F = 4-5 pN, the nucleosomes are significantly unwrapped. (These forces are well below the tension produced by RNA polymerase; therefore, the observed unwrapping corresponds to 'native' conditions.) Importantly, the nucleosome breathing occurs asymmetrically, with one end opened much stronger than the other one. We were able to explain this non-trivial effect theoretically, taking into account a non-linear adhesion energy function describing interactions between DNA and histone core. This observation may have profound implications for transcription and other DNA-related cellular functions. According to our data, asymmetric unwrapping of nucleosomal DNA exposes 50-60 bp at one end (compared to 20-30 bp at both ends in the case of symmetric unwrapping). Therefore, asymmetric breathing of nucleosomes increases accessibility of DNA to TFs. These considerations are critical for designing and interpreting the experiments on TF binding to chromatin.